Controlled melting and solidification in encapsulated phase change materials (PCMs) is of practical interest, for example, in latent heat storage applications. The choice of PCMs and the dynamic heat transfer characteristics during phase change - affecting the transient charging/discharging rates - are decisive for the energy and power density of the heat storage option. For example, highly conductive, high melting point (above 700 K) metal alloys have a potential advantage as a high energy and power density latent heat storage, compared to the widely used low conducting molten salt and paraffin wax. This advantage depends on the relative dominance of heat transfer modes that vary depending on the thermal properties of the PCM, shape of the encapsulation, and the load conditions, and must be quantified to warrant a fair comparison. We developed a 2D transient phase change model of encapsulated PCMs, accounting for phase change over a temperature range, volumetric expansion and contraction, and multi-mode heat transfer within the encapsulated PCM. The enthalpy-porosity method was used to model the phase change in a fixed grid. Validation was performed with literature data of low and high-conductivity PCM experiments (RT27 and lead). Two types of PCMs were subsequently investigated in detail: a high-conducting binary-eutectic alloy Al-12.6Si and a low-conducting commercially available RT27 paraffin wax (Rubitherm GmbH). The model was used to compare the phase change process and the strength of the various modes of heat transfer in the PCM filled cylindrical stainless-steel encapsulations in horizontal and vertical orientation with constant temperature walls. A full parameter study and non-dimensional analysis are presented for different PCMs. The results quantified the influence of boundary conditions, thermophysical properties and geometrical parameters on the phase change process and the contribution of the natural convection within the encapsulation. The non-dimensional analysis linked the melt fraction and heat transfer rates to a combination of the Fourier, Stefan, Rayleigh and Nusselt numbers. Fitting of the exponents of non-dimensional number groups to the heat transfer calculations allowed to provide general correlations for melting time, melt fraction, heat transfer rates, and characteristics of melting. Such correlations provide general understanding of the transient heat transfer in phase change media and provide engineering tools for designing, for example, a latent heat storage unit.